Remarks on the existence of Spinning Membrane Actions

Abstract

It has been recently argued by some authors that is impossible to construct a Weyl invariant spinning membrane action, where the $S$-supersymmetry associated with the 3D superconformal algebra, is relinquished without gauge fixing. Contrary to those assertions, we show why it is possible to construct a Weyl-invariant spinning polynomial membrane action, without curvature terms,where $both$ the conformal boost symmetry and $S$-supersymmetry are explicitly broken by the action. It is shown that the gauge algebra $closes$ despite that the two latter symmetries are broken . For this to happen, a modifed $Q$-supersymmetry transformation, a sort of new $Q+K+S$ ``sum `` rule, is required that generates the compensating terms to cancel the spurious contributions fromthe $S$ and conformal boost anomalous transformations. A substantial discussion of the quantization of the spinning membrane and anomalies is given. We review briefly the role that this spinning membrane action may have in the theory of $D$-branes, Skyrmions and BPS monopoles in the large $N$-limit of SU(N) Yang-Mills .